Sounds like you have a clutch MC rebuild in your immediate future. There's a rubber valve seal inside there that may be partialy leaking past which would result in the problem you describe, on the second go it's expanding enough to work properly.
If the cylinder isn't scored or rusty then you can just rebuild it with a $15 rebuild kit otherwise it's $100 for a replacement.
I rebuilt my clutch MC in about 2 hours, a good chunk of which time is spent underneath the car trying to bleed all the air out. Might as well do the slave cylinder rebuild while you're at it.